색상 차이 공식

1 개요

color difference, color distance

[math]\displaystyle{ \Delta E }[/math]

색상 차이, 색상 거리

• 두 색상의 차이
• 두 색이 색공간에서 떨어진 거리

2 CIE76

• Lab 색공간에서의 거리

[math]\displaystyle{ \Delta E_{76}^* = \sqrt{ (L^*_2-L^*_1)^2+(a^*_2-a^*_1)^2 + (b^*_2-b^*_1)^2 } }[/math]

3 CIE94

• CIELCH 개념에 따른 보정

[math]\displaystyle{ \Delta E_{94}^* = \sqrt{ \left(\frac{\Delta L^*}{k_L S_L}\right)^2 + \left(\frac{\Delta C^*_{ab}}{k_C S_C}\right)^2 + \left(\frac{\Delta H^*_{ab}}{k_H S_H}\right)^2 } }[/math]

여기서:

[math]\displaystyle{ \Delta L^* = L^*_1 - L^*_2 }[/math]

[math]\displaystyle{ C^*_1 = \sqrt{ {a^*_1}^2 + {b^*_1}^2 } }[/math]

[math]\displaystyle{ C^*_2 = \sqrt{ {a^*_2}^2 + {b^*_2}^2 } }[/math]

[math]\displaystyle{ \Delta C^*_{ab} = C^*_1 - C^*_2 }[/math]

[math]\displaystyle{ \Delta H^*_{ab} = \sqrt{ {\Delta E^*_{ab}}^2 - {\Delta L^*}^2 - {\Delta C^*_{ab}}^2 } = \sqrt{ {\Delta a^*}^2 + {\Delta b^*}^2 - {\Delta C^*_{ab}}^2 } }[/math]

[math]\displaystyle{ \Delta a^* = a^*_1 - a^*_2 }[/math]

[math]\displaystyle{ \Delta b^* = b^*_1 - b^*_2 }[/math]

[math]\displaystyle{ S_L = 1 }[/math]

[math]\displaystyle{ S_C = 1+K_1 C^*_1 }[/math]

[math]\displaystyle{ S_H = 1+K_2 C^*_1 }[/math]

단,

[math]\displaystyle{ k_L=1, K_1=0.045, K_2=0.015 }[/math] (그래픽 아트의 경우)

[math]\displaystyle{ k_L=2, K_1=0.048, K_2=0.014 }[/math] (직물의 경우)

4 CIE2000

[math]\displaystyle{ \Delta E_{00}^* = \sqrt{ \left(\frac{\Delta L'}{k_L S_L}\right)^2 + \left(\frac{\Delta C'}{k_C S_C}\right)^2 + \left(\frac{\Delta H'}{k_H S_H}\right)^2 + R_T \frac{\Delta C'}{k_C S_C}\frac{\Delta H'}{k_H S_H} } }[/math]

[math]\displaystyle{ \Delta L^\prime = L^*_2 - L^*_1 }[/math]

[math]\displaystyle{ \bar{L} = \frac{L^*_1 + L^*_2}{2} }[/math], [math]\displaystyle{ \bar{C} = \frac{C^*_1 + C^*_2}{2} }[/math]

[math]\displaystyle{ a_1^\prime = a_1^* + \frac{a_1^*}{2} \left( 1 - \sqrt{\frac{\bar{C}^7}{\bar{C}^7 + 25^7}} \right) }[/math], [math]\displaystyle{ a_2^\prime = a_2^* + \frac{a_2^*}{2} \left( 1 - \sqrt{\frac{\bar{C}^7}{\bar{C}^7 + 25^7}} \right) }[/math]

[math]\displaystyle{ \bar{C}^\prime = \frac{C_1^\prime + C_2^\prime}{2} }[/math], [math]\displaystyle{ \Delta{C'}=C'_2-C'_1 }[/math]

[math]\displaystyle{ C_1^\prime = \sqrt{a_1^{'^2} + b_1^{*^2}} }[/math], [math]\displaystyle{ C_2^\prime = \sqrt{a_2^{'^2} + b_2^{*^2}} }[/math]

[math]\displaystyle{ h_1^\prime=\text{atan2} (b_1^*, a_1^\prime) \mod 360^\circ }[/math], [math]\displaystyle{ h_2^\prime=\text{atan2} (b_2^*, a_2^\prime) \mod 360^\circ }[/math]

[math]\displaystyle{ \Delta h' = \begin{cases} h_2^\prime - h_1^\prime & \left| h_1^\prime - h_2^\prime \right| \leq 180^\circ \\ h_2^\prime - h_1^\prime + 360^\circ & \left| h_1^\prime - h_2^\prime \right| \gt 180^\circ, h_2^\prime \leq h_1^\prime \\ h_2^\prime - h_1^\prime - 360^\circ & \left| h_1^\prime - h_2^\prime \right| \gt 180^\circ, h_2^\prime \gt h_1^\prime \end{cases} }[/math]

[math]\displaystyle{ \Delta H^\prime = 2 \sqrt{C_1^\prime C_2^\prime} \sin (\Delta h^\prime/2) }[/math]

[math]\displaystyle{ \bar{H}^\prime=\begin{cases} (h_1^\prime + h_2^\prime + 360^\circ)/2 & \left| h_1^\prime - h_2^\prime \right| \gt 180^\circ \\ (h_1^\prime + h_2^\prime)/2 & \left| h_1^\prime - h_2^\prime \right| \leq 180^\circ \end{cases} }[/math]

[math]\displaystyle{ T = 1 - 0.17 \cos ( \bar{H}^\prime - 30^\circ ) + 0.24 \cos (2\bar{H}^\prime) + 0.32 \cos (3\bar{H}^\prime + 6^\circ ) - 0.20 \cos (4\bar{H}^\prime - 63^\circ) }[/math]

[math]\displaystyle{ S_L = 1 + \frac{0.015 \left( \bar{L} - 50 \right)^2}{\sqrt{20 + {\left(\bar{L} - 50 \right)}^2} } \quad S_C = 1+0.045 \bar{C}^\prime \quad S_H = 1+0.015 \bar{C}^\prime T }[/math]

[math]\displaystyle{ R_T = -2 \sqrt{\frac{\bar{C}'^7}{\bar{C}'^7+25^7}} \sin \left[ 60^\circ \cdot \exp \left( -\left[ \frac{\bar{H}'-275^\circ}{25^\circ} \right]^2 \right) \right] }[/math]

5 같이 보기

• CEILAB
• 색상 변환
• 색상
• 차이
• 거리

7 참고 자료

• http://en.wikipedia.org/wiki/Color_difference